Frequency manipulation, including clock/frequency generation and synthesizing, is of key importance for modern electronic devices. For example, sequential logic circuits, e.g., processors and controllers, need to be triggered by clocks for proper operation; and transmitters, receivers and/or transceivers of communication, network, broadcasting and/or positioning systems require signals of specific frequencies for signal processing, modulation and/or demodulation, etc.
Frequency multiplication, which is proved to be very useful for frequency manipulation, aims to provide an output signal whose frequency is a multiple of an input frequency, i.e., the frequency of the output signal equals a product of a multiplication factor and the input frequency. One prior art approach of frequency multiplication manages to provide a multiplication factor of 2 or 4/3 by digital operations if an in-phase signal of the input frequency and a quadrature phase signal of the input frequency are both available; however, this approach lacks flexibility since it fails to provide multiplication factors of arbitrary numbers. Another prior art approach provides multiplication factors of even numbers, but not odd numbers.
Still another prior art approach utilizes analog mixing to implement frequency multiplication, but such an approach suffers from undesired harmonics. Low frequency harmonics or inter-modulation are difficult to be filtered out, and will cause spurious signals in the circuit. Though harmonics of high frequencies can be filtered out by inductor-capacitor (LC) tank or resistor-capacitor (RC) tank circuit, such additional filtration has the disadvantages of large layout areas and high cost. Additionally, the output frequency for an LC tank circuit is the LC resonant frequency which is strongly dependent on the implemented LC value, and thus hard to be programmable.